Nose breathing leaks to mouth

Sometimes when I am breathing (exhaling) through my nose with my mouth closed I feel air pressure in my mouth, trying to escape through my lips. If I move my tongue away from the roof of my mouth I can feel my lips puff out. If I pinch my nose closed and try to breathe out it seems to clear the problem. This happens even though my nasal passages are clear. It is most noticeable at night and I assume it relates to the fact that I often wake up during the night and find that I have been mouth breathing - a very dry mouth. The problem I really want to address is the mouth breathing when sleeping, not sure if the "leakage" from nose to mouth is the cause or even related but I haven't found anything online that sounds like my problem.